That would be your county's family court.What court would have that order mentioned and used by the parent those 35+ years ago.
I suggest you make a personal visit to the records section and have a search done for your parents' divorce case file.
Once you have located the divorce decree and the name change document (could be the same document) get several certified copies and keep them in your permanent files.
You aren't likely to be able to get your birth certificate changed without a court order but the documentation allowing the change from A to B should be enough to justify a "common law" name change, especially now that you've been an adult using the name B all these years.
There really isn't anything to sort out but if you want something official to set your mind to rest, the Ohio adult name change process is rather simple and it'll get you a court order acknowledging that your name is officially changed from A to B and could allow you to amend your birth certificate as well.
See:
http://probate.cuyahogacounty.us/pdf...ange_Adult.pdf
You can get a form like that from your own county Probate Court or create one on your computer with your local court's information.

